For x>0, lim_(xrightarrow 0) [(sin x)^(1/x)+(1/x)^(sin x)]= A)= B)-1 C)1 D)2

Karson Maddox

Karson Maddox

Answered question

2023-01-29

For x > 0 , lim x 0 [ ( sin x ) 1 x + ( 1 x ) sin x ] =
A)0
B)-1
C)1
D)2

Answer & Explanation

Trinity Mack

Trinity Mack

Beginner2023-01-30Added 3 answers

The right decision is C 1
Discover the value of lim x 0 [ ( sin x ) 1 x + ( 1 x ) sin x ]
According to question
For x>0
lim x 0 ( sin x ) 1 / x + lim x 0 ( 1 x ) sin x = e lim x 0 log sin x x + e lim x 0 ( log x cos e c x )
= e + e lim x 0 ( 1 x cos e c x cot x )       [ x > 0 , log sin x = ]
= 0 + e lim x 0 ( tan x x sin x )       [ e = 0 ]
= e 0 [ sin 0 = 0 ]
1
Thus, Option ‘C’ is right.

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